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Analysis of Kelly betting on finite repeated games

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  • Wu, Mu-En
  • Tsai, Hui-Huang
  • Chung, Wei-Ho
  • Chen, Chien-Ming

Abstract

The Kelly criterion can be used to maximize returns in a game with win rate p and odds b; however, optimization theoretically requires wagering over an infinite number of time steps. Despite the fact that Kelly's theory has been extended to most of the trading strategies used in financial markets, there is still a large gap between the theoretical determination of optimal bidding fractions and practical application of these methods. In this paper, we illustrate the difference between the theoretical and simulation results obtained from a gambling situation involving a finite number of bidding steps T( = W + L), where W and L respectively denote the numbers of wins and losses. The optimal bidding fraction based on the Kelly criterion should employ the win\loss proportion W/T rather than the win rate p; however, it is not possible to obtain the value of a priori. W. Thus, profits under the Kelly formula are calculated by applying win rate p and the win\lose proportion W/T. In this paper, we denote pt as the current win\lose proportion before time step t as an alternative to win rate p. The proposed approach does away with the need to apply win rate p and produces profits that are nearly optimal under Kelly betting.

Suggested Citation

  • Wu, Mu-En & Tsai, Hui-Huang & Chung, Wei-Ho & Chen, Chien-Ming, 2020. "Analysis of Kelly betting on finite repeated games," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    • Handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319310203
    DOI: 10.1016/j.amc.2019.125028
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    References listed on IDEAS

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    1. Michael Stutzer, 2011. "On Growth-Optimality vs. Security Against Underperformance," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 44, pages 641-653, World Scientific Publishing Co. Pte. Ltd..
    2. John M. Mulvey & Mehmet Bilgili & Taha M. Vural, 2011. "A Dynamic Portfolio of Investment Strategies: Applying Capital Growth with Drawdown Penalties," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 50, pages 735-751, World Scientific Publishing Co. Pte. Ltd..
    3. Chung-Han Hsieh & B. Ross Barmish, 2017. "On Drawdown-Modulated Feedback Control in Stock Trading," Papers 1710.01503, arXiv.org.
    4. Mu-En Wu & Wei-Ho Chung, 2019. "Empirical Evaluations on Momentum Effects of Taiwan Index Futures via Stop-Loss and Stop-Profit Mechanisms," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 629-648, March.
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    Cited by:

    1. Mu-En Wu & Jia-Hao Syu & Chien-Ming Chen, 2022. "Kelly-Based Options Trading Strategies on Settlement Date via Supervised Learning Algorithms," Computational Economics, Springer;Society for Computational Economics, vol. 59(4), pages 1627-1644, April.
    2. Chung-Han Hsieh, 2021. "On Asymptotic Log-Optimal Buy-and-Hold Strategy," Papers 2103.04898, arXiv.org.

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